Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

Large‐Area Aminated‐Graphdiyne Thin Films for Direct Methanol Fuel Cells

A two‐dimensional (2D) carbon nanofilm with uniform artificial nanopores is an ideal material to ultimately suppress the fuel permeation in the proton exchange membrane fuel cells. Graphdiyne has great mechanical strength, high dimensional stability, and controllable nanopores, and has good prospects to play this crucial role. It is found that graphdiyne nanofilm with amino groups and natural nanopores can be easily prepared with high integrity. The aminated graphdiyne has good compatibility with the Nafion matrix owing to the acid–base interaction between them. The excellent comprehensive properties of graphdiyne in selectivity, dimensional stability, and integrity effectively improve the power performance and stability of fuel cells at wide temperature. Our results can be developed into a universal method that can easily realize the selective separation of ions and small molecules, and open a new way for the emerging applications in green energy.     

Numerical analysis of the wrinkling behavior of thin membranes

Archive of Applied Mechanics - Membranes are widely applied in the large-span buildings and spatial deployable structures. They are prone to wrinkle under compression due to their small bending...     

A stable pillared metal–organic framework constructed by H4TCPP ligand as luminescent sensor for selective detection of TNP and Fe3+ ions

A novel luminescent metal–organic framework ( Zn‐TCPP/BPY ) with pillared structure based on 2,3,5,6‐tetrakis(4‐carboxyphenyl)pyrazine (H₄TCPP) and 4,4′‐bipyridine (BPY) has been designed and synthesized through a solvothermal reaction. The [Zn₂(COO)₄] paddlewheel units are linked by TCPP^4? ligands to form two‐dimensional layers and further connected by BPY ligands as pillars to construct the twofold interpenetrating three‐dimensional framework. Interestingly, Zn‐TCPP/BPY possesses outstanding stability in organic solvents and water as well as maintains its structural rigidity in aqueous solutions of different pH values (3–12). After activation, Zn‐TCPP/BPY possesses permanent porosity with Brunauer–Emmett–Teller surface area of 630 m² g^–1. Remarkably, Zn‐TCPP/BPY displays excellent fluorescent property in virtue of the aggregation‐induced emission effect of the H₄TCPP ligand, which can be highly active and quenched by small amounts of 2,4,6‐trinitrophenol (TNP) and Fe³⁺ ions. Furthermore, the detection effect of Zn‐TCPP/BPY remains basically the same even after five cycles. The excellent stability, high sensitivity, and recyclability of Zn‐TCPP/BPY make it an outstanding chemical sensor for detecting TNP and Fe³⁺ ions.     

A Potential Alternative to Polystyrene: Ring-opening Terpolymerization of Different Epoxides with Phthalic Anhydride Using Metal-free Dual Catalysts

A series of semi-aromatic polyesters named as Poly(PO-CHO-PA) were facilely synthesized via ring-opening terpolymerization of biobased cyclohexane oxide(CHO)/propylene oxide(PO)/phthalic anhydride(PA) using economical U1/PPNCl as dual catalyst. The proportion of CHO-PA and PO-PA segments in polymer can be readily altered by changing the feed ratio of CHO/PO because the reactivity ratios of CHO and PO with PA calculated by Fineman-Ross method are comparable. All synthesized amorphous polyesters with various compositions show one Tg ranging from 62 ℃ to 133 ℃. Significantly, the mechanical, thermal and barrier properties of these amorphous semi-aromatic polyesters are also adjustable and investigated for the first time. The results indicate the semi-polyesters exhibit superior thermostability(T5% ranging from 306 ℃ to323 ℃) and high tensile strength(40.21-55.7 MPa) that is comparable with polystyrene(PS). Furthermore, Poly(PO-CHO-PA) films possess a promising prospect as packaging materials because of its colorless and highly transparent nature, along with low oxygen and water vapor transmission rate. All above performances may guarantee its potential alternative to commercial PS.     

80.5 MeV/u碳离子诱发铜靶的放射性剩余产物测量

高能重带电粒子能直接穿透靶原子核外电子层,与原子核发生直接碰撞,发生散裂反应,产生一系列具有放射性的剩余产物核.重带电粒子诱发靶材放射性剩余核与辐射防护和人员安全有着密切联系,当前,大部分剩余核产额主要依靠蒙特卡罗粒子输运程序进行模拟计算,其准确程度亟需通过实验测量进行准确评估.本文利用能量为80.5 MeV/u的(12)^C⁶⁺粒子对薄铜靶开展了辐照实验与伽玛射线测量,结合伽玛谱学分析方法,得出了辐照产生的18种放射性剩余产物的初始活度和产生截面值,并与PHITS模拟结果进行对比.结果表明,PHITS模拟程序对放射性剩余核种类的估计具有较高可靠性,在其绝对产额方面,与实验测量仍具有较大偏差.     

原子系综中光学腔增强的Duan-Lukin-Cirac-Zoller写过程激发实验

原子系综中的Duan-Lukin-Cirac-Zoller(DLCZ)过程是产生光与原子(量子界面)量子关联和纠缠的重要手段.当一束写光与原子发生作用时,将会产生斯托克斯(Stokes)光子的自发拉曼散射,并同时产生一个自旋波(spin-wave)存储在原子系综中,上述过程即为DLCZ量子记忆产生过程.这一过程被广泛地研究.本文将87Rb原子系综放入驻波腔,并使Stokes光子与光学腔共振,我们观察到有腔且锁定的情况下Stokes光子产生概率比无腔时增大了8.7倍.在此条件下研究了Stokes光子产生概率和写光功率的关系,Stokes光子产生概率随写光功率线性增大.     

A no expanding breather theorem for noncompact Ricci flows

Annals of Global Analysis and Geometry - In this note we show that, under certain curvature positivity conditions (the weak $${\text {PIC}}-2$$ condition or the nonnegative bisectional curvature...     

Practical algorithm substitution attack on extractable signatures

Designs, Codes and Cryptography - An algorithm substitution attack (ASA) can undermine the security of cryptographic primitives by subverting the original implementation. An ASA succeeds when it...